[tex]N=1000w+100x+10y+z\\
w=z=1\\
x,y\in\{0,1,2,\ldots,7,8,9\}\\
10x+y=\frac{N}{21}\\
10x+y=\frac{1000w+100x+10y+z}{21}\\
10x+y=\frac{1000+100x+10y+1}{21}\\
10x+y=\frac{100x+10y+1001}{21}\\
210x+21y=100x+10y+1001\\
110x+11y-1001=0\\
10x+y-91=0\\
y=-10x+91\\\\
\hbox{The above equation meets the condition }x,y\in\{0,1,2,\ldots,7,8,9\}\\
\hbox{only for } x=9:\\
y=-10\cdot9+91\\
y=-90+91\\
y=1\\\\
\hbox{Therefore:}\\
N=1000\cdot1+100\cdot9+10\cdot1+1\\
N=1000+900+10+1\\
N=\boxed{1911}
[/tex]
